Cold Air is Dense

Introduction:

We wish to set up a learning situation in which students will
discover, through the examination and manipulation of real data
from a natural environment, that:

air has mass and density, and

cold air is denser than warm air.

These insights are absolutely fundamental to understanding
virtually everything about weather and climate. Until a student has
his or her mind firmly around these two concepts, he or she is not
ready to understand how storms work, not ready to understand why
the prevailing winds blow the way they do, not ready to understand
why deserts occur where they do.

Although these two concepts are fundamental underpinnings
of virtually every physical process in the atmosphere, they are not
intuitively obvious--in fact, they are counter-intuitive. The student
looks around at the air skeptically-- if there are so many molecules in
that air, why can't we see them? If air has weight, why doesn't it
register on a scale? On hot summer nights, the air feels oppressive,
heavy--don't tell me that hot August air is low density "Air has
mass", "air has density", and "cold air is dense" are the kinds of
statements that students tend to memorize and parrot back, without
actually altering their world-view, because these statements don't fit
with their day-to-day experience of real-life air.

Because an understanding of the relationship between
density and temperature of air is fundamental to so many natural
processes, yet is counter-intuitive, it is a good investment of
student and instructor time to construct this understanding upwards
from a solid basis in the observation of real data.

Insights/Curriculum Highlights:

Air is made of molecules, and therefore has mass.

Barometric pressure is a measure of how much mass of air,
i.e. how many air molecules, exist above the point of
measurement, all the way up to the top of the atmosphere.

Therefore, barometric pressure decreases with elevation.

Any given volume of air has density. The density of air can
vary from place to place and from time to time.

The difference in barometric pressure between observation
sites at different elevations is a measure of the density of air in
a column of air between those two elevations.

Cold air is denser than warm air.

Thinking Skills / Pedagogical Highlights:

Making a connection between laboratory scale observations
and atmosphere-scale data sets.

Drawing on hands-on observations to explain an aspect of a
natural system.

Thinking about a phenomenon (density of air) that is invisible.

Imagining boundaries or limits, and thinking about phenomena
within those boundaries (a column of air, a parcel of air)

Linking properties that are detectable to the human senses (e.g.
air temperature) with molecular scale phenomena (molecules
per volume of air).

Linking properties that are measurable at the macroscopic scale
(e.g. barometric pressure) to molecular scale phenomena
(number of molecules).

Building a chain of reasoning from cause to effect.

Building a chain of reasoning from observation to
interpretation.

Using time series graphs; comparing how different parameters
vary through time.

Recognizing that a measurable property varies through time
(barometric pressure rises and falls as weather systems pass)
and also through space (barometric pressure decreases with
increasing elevation).

Recognizing covariance: two properties varying in the same
direction under the influence of the same circumstances
(barometric pressure at the Open Lowland site covaries with
that at the Ridgetop site).

Using a scatterplot; thinking about two or three data
parameters simultaneously.

Procedure:

1. Introductory Hands-on Investigation: Make a Barometer

Students create home made barometers and discuss how they
work. Instructions for this activity are contained in many
middle school science books. See, for example: R. L. Bonnet and G. D. Keen, Earth Science: 49 Science Fair Projects, TAB Books, 1990, pp. 127-131.

2. Video : Torricelli's discovery of air pressure

Students view and discuss the section of the "Connections"
video in which Torricelli's discovery of air pressure is
illustrated. In this video, a mercury barometer is carried up a
mountainside, and the mercury is seen to fall as the climber
ascends. (Alternatively, students can read a description of the
same discovery in the book Connections by James Burke,
1978, Little, Brown & Co, Boston, pp. 74-17.)

The interpretation is that the weight of the mercury balances
the weight of the overlying air. The weight of the overlying
air decreases as the climber rises higher in the atmosphere;
thus less weight of mercury is needed to balance the
diminished weight of the overlying air.

3: Reproduce Torricelli's experiment in a tall building

Using a handheld barometer, students will measure the
barometric pressure at street level. Then, emulating the
experimenter in the "Connections" video, they will climb the
stairs or ascend the elevator of a tall building, measuring
barometric pressure at each landing or at several stops along
the way.

They observe that the air pressure at the street level is higher than at rooftop
level (figure 1). For a twelve story building the
difference in air pressure is about 4 mb. The building needs to be at least
8 stories high to register an unambiguous barometric pressure difference.

4. Data-based investigation: barometric pressure from BRF

Students examine barometric pressure data sets that were recorded at Open
Lowland and Ridgetop sensor sites at Black Rock Forest. (figure
2). Display should be zoomed so that a month of two at a time is visible.
Each pair of students can be responsible for several months of data. Data
can be printed out and scotch taped together to form a long time series of
a year or more duration. (If printouts from different students are combined,
be sure that all students set the plot vertical scale the same.)

Points to observe:

Over time, the barometric pressure at each site goes up
and down, up and down. The periodicity is about a
week, but the pattern is not very regular.

Barometric pressure at the Ridgetop site is always less
than at the Open Lowland site.

Barometric pressure at Ridgetop and at Open Lowland
covary: in other words, when one goes up, the other
goes up; when one goes down, the other goes down.

The difference between the barometric pressure at
Ridgetop and Open Lowland is larger than the difference
between the high and low pressures at either Ridgetop or
Open Lowland. In other words, the variability in space
is greater than the variability in time in this data set.

Points to figure out and/or discuss:

The up and down wiggles of each barometric pressure
record reflect weather systems passing across the field
area. (This could be the subject of a separate
investigation, in which students discover the relationship
between barometer trends and sunny or rainy weather.)

Barometric pressures at the two sites covary because they
are subject to the same weather systems.

Which site do you think is at higher elevation? Think
about the hands-on experiment with the hand-held
barometer, and about the experimenter in the connections
video. The Ridgetop Site must be at higher elevation
than the Open Lowland Site because it always has a
lower barometric pressure. Ridgetop has a lower
barometric pressure than Open Lowland because fewer
molecules of air lie between the Ridgetop site and the top
of the atmosphere than lie between the Open Lowland
site and the top of the atmosphere.

We normally think about barometric pressure variation in
the context of changes through time ("the barometer is
falling" or "the barometer is rising"), related to the
passage of weather systems. Quantitatively, however,
the spatial variation of barometric pressure with elevation
is larger than the temporal variation at any given site.

(Optional) Using your results from the hands-on investigation
with the barometer and the tall building, plus your
observations of barometric pressure at Black Rock Forest,
estimate the difference in elevation between the Ridgetop Site
and the Open Lowland Site.

Returning to the long time series of barometric pressure versus
time over the course of the year, students will observe that the
pressure difference between the ridgetop and lowland is not
always exactly the same. The difference in pressure between
the two sites is a measure of the mass or density of the column
of air in between the lower and higher elevations. What is
changing the density of the column of air between the ridgetop
and lowland elevations?

Students examine digital photographs recorded at the same time and place each
week. Each student or student pair is responsible for one day of data, with
data sets spaced one or two weeks apart (the entire class should span half
a year of data). For their day, each student-pair assembles a sheet of paper
with the digital photograph, plus a number representing the difference between
the barometric pressure recorded at the ridgetop and the lowland stations
on their day (figure 3). The sheets of paper will
then be arranged along a wall in order from lowest to highest number; i.e.
in order from least dense to most dense column of air between ridgetop and
lowland elevations.

The students will then examine the photographs, looking for patterns or trends.
We anticipate that the students will observe that the snowy cold-looking photographs
are clustered at the high air-density end of the continuum, and the summery
hot- looking photographs are clustered at the low air-density end of the continuum
(figure 3).

Students try to explain the relationship between the time of year and the
density of the column of air. Teacher guides discussion with examples of materials
that become less dense as they get warmer, for example mercury in a barometer.
Class eventually hypothesizes that a cold column of air is more dense than
a warm column of air (figure 4).

(for strong high school students or undergraduates) Students test the hypothesis
(figure 4) that cold air is denser than warm air,
and that this is why the difference in barometric pressure between the Ridgetop
and Open Lowland site is larger is cold weather. They make a graph showing
the air temperature as the independent variable, and the difference between
barometric pressure at Open Lowland and Ridgetop as the independent variable.
(figure 5). The difference in barometric pressure
between the Open Lowland site and the Ridgetop site is a measure of the mass
or density of the column of air between the two elevations.

Students observe a strong correlation between temperature and barometric pressure
difference (figure 5). This supports the hypothesis
that air temperature is influencing the weight (density) of the column of
air between the ridgetop and lowland elevations.

Teacher can discuss this observation in terms of the behavior
of gas molecules in response to heating or cooling.

Created by Kim Kastens, Lamont-Doherty Earth Observatory
(kastens@ldeo.columbia.edu).
May be freely used for educational purposes provided appropriate credit is
given.